[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki41\/order-7-cubic-honeycomb-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki41\/order-7-cubic-honeycomb-wikipedia\/","headline":"Order-7 cubic honeycomb – Wikipedia","name":"Order-7 cubic honeycomb – Wikipedia","description":"before-content-x4 From Wikipedia, the free encyclopedia after-content-x4 In the geometry of hyperbolic 3-space, the order-7 cubic honeycomb is a regular","datePublished":"2018-02-01","dateModified":"2018-02-01","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki41\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki41\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a2\/Schlegel_wireframe_8-cell.png\/60px-Schlegel_wireframe_8-cell.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a2\/Schlegel_wireframe_8-cell.png\/60px-Schlegel_wireframe_8-cell.png","height":"60","width":"60"},"url":"https:\/\/wiki.edu.vn\/en\/wiki41\/order-7-cubic-honeycomb-wikipedia\/","about":["Wiki"],"wordCount":4276,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4From Wikipedia, the free encyclopedia       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4In the geometry of hyperbolic 3-space, the order-7 cubic honeycomb is a regular space-filling tessellation (or honeycomb). With Schl\u00e4fli symbol {4,3,7}, it has seven cubes {4,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many cubes existing around each vertex in an order-7 triangular tiling vertex arrangement.       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Table of ContentsRelated polytopes and honeycombs[edit]Order-8 cubic honeycomb[edit]Infinite-order cubic honeycomb[edit]See also[edit]References[edit]External links[edit]Related polytopes and honeycombs[edit]It is one of a series of regular polytopes and honeycombs with cubic cells: {4,3,p}:{4,3,p} polytopesSpaceS3H3FormFiniteCompactParacompactNoncompactName{4,3,3}{4,3,4}{4,3,5}{4,3,6}{4,3,7}{4,3,8}… {4,3,\u221e}ImageVertexfigure{3,3}{3,4}{3,5}{3,6}{3,7}{3,8}{3,\u221e}It is a part of a sequence of hyperbolic honeycombs with order-7 triangular tiling vertex figures, {p,3,7}.{3,3,7}{4,3,7}{5,3,7}{6,3,7}{7,3,7}{8,3,7}{\u221e,3,7}Order-8 cubic honeycomb[edit]Order-8 cubic honeycombTypeRegular honeycombSchl\u00e4fli symbols{4,3,8}{4,(3,8,3)}Coxeter diagrams = Cells{4,3} Faces{4}Edge figure{8}Vertex figure{3,8}, {(3,4,3)}Dual{8,3,4}Coxeter group[4,3,8][4,((3,4,3))]PropertiesRegularIn the geometry of hyperbolic 3-space, the order-8 cubic honeycomb a regular space-filling tessellation (or honeycomb). With Schl\u00e4fli symbol {4,3,8}. It has eight cubes {4,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many cubes existing around each vertex in an order-8 triangular tiling vertex arrangement.       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4It has a second construction as a uniform honeycomb, Schl\u00e4fli symbol {4,(3,4,3)}, Coxeter diagram, , with alternating types or colors of cubic cells.Infinite-order cubic honeycomb[edit]Infinite-order cubic honeycombTypeRegular honeycombSchl\u00e4fli symbols{4,3,\u221e}{4,(3,\u221e,3)}Coxeter diagrams = Cells{4,3} Faces{4}Edge figure{\u221e}Vertex figure{3,\u221e}, {(3,\u221e,3)}Dual{\u221e,3,4}Coxeter group[4,3,\u221e][4,((3,\u221e,3))]PropertiesRegularIn the geometry of hyperbolic 3-space, the infinite-order cubic honeycomb a regular space-filling tessellation (or honeycomb). With Schl\u00e4fli symbol {4,3,\u221e}. It has infinitely many cubes {4,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many cubes existing around each vertex in an infinite-order triangular tiling vertex arrangement.It has a second construction as a uniform honeycomb, Schl\u00e4fli symbol {4,(3,\u221e,3)}, Coxeter diagram, , with alternating types or colors of cubic cells.See also[edit]References[edit]Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN\u00a00-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp.\u00a0294\u2013296)The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN\u00a099-35678, ISBN\u00a00-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space) Table IIIJeffrey R. Weeks The Shape of Space, 2nd edition ISBN\u00a00-8247-0709-5 (Chapters 16\u201317: Geometries on Three-manifolds I,II)George Maxwell, Sphere Packings and Hyperbolic Reflection Groups, JOURNAL OF ALGEBRA 79,78-97 (1982) [1]Hao Chen, Jean-Philippe Labb\u00e9, Lorentzian Coxeter groups and Boyd-Maxwell ball packings, (2013)[2]Visualizing Hyperbolic Honeycombs arXiv:1511.02851 Roice Nelson, Henry Segerman (2015)External links[edit]     (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki41\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki41\/order-7-cubic-honeycomb-wikipedia\/#breadcrumbitem","name":"Order-7 cubic honeycomb – Wikipedia"}}]}]